Since age and sex play an important role in transmission of diseases, we propose a SIR (susceptible-infectious-recovered) model for short-term predictions where the population is divided into subgroups based on both factors without taking into account vital dynamics. After stating our model and its underlining assumptions, we analyze its qualitative behavior thoroughly. We prove global existence and uniqueness, non-negativity, boundedness and certain monotonicity properties of the solution. Furthermore, we develop an explicit-implicit numerical solution algorithm and show that all properties of the continuous solution transfer to its time-discrete version. Finally, we provide one numerical example to illustrate our theoretical findings.

中文翻译：

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年龄和性别结构的SIR模型：理论和隐式数值解算法

由于年龄和性别在疾病传播中起着重要作用，因此我们提出了一种SIR（易感感染恢复）模型，用于短期预测，在该模型中，根据这两个因素将人口分为亚组，而不考虑生命动态。在陈述了我们的模型及其重要假设之后，我们将彻底分析其定性行为。我们证明了该解的整体存在性和唯一性，非负性，有界性和某些单调性。此外，我们开发了显式-隐式数值解算法，并证明了连续解的所有属性都将转换为时间离散形式。最后，我们提供一个数值示例来说明我们的理论发现。